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On reversible automata

Abstract : A reversible automaton is a finite (possibly incomplete) automaton in which each letter induces a partial one-to-one map from the set of states into itself. We give four non-trivial characterizations of the languages accepted by a reversible automaton equipped with a set of initial and final states and we show that one can effectively decide whether a given rational (or regular) language can be accepted by a reversible automaton. The first characterization gives a description of the subsets of the free group accepted by a reversible automaton that is somewhat reminiscent of Kleene's theorem. The second characterization is more combinatorial in nature. The decidability follows from the third -- algebraic -- characterization. The last characterization relates reversible automata to the profinite group topology of the free monoid.
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Contributor : Jean-Eric Pin Connect in order to contact the contributor
Submitted on : Thursday, March 2, 2006 - 7:00:07 PM
Last modification on : Saturday, March 28, 2020 - 2:19:16 AM
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  • HAL Id : hal-00019977, version 1




Jean-Eric Pin. On reversible automata. Proceedings of the first LATIN conference, 1992, Saõ-Paulo, Brazil. pp.401-416. ⟨hal-00019977⟩



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